Tail amplitude as a measure of portfolio risk

Abstract

This paper presents a generalization of the traditional covariance definition of risk to generate an optimal portfolio of foreign exchange rates. Based on the empirical observation that the tails of the distribution of fluctuations in exchange rates behave as a power law across different markets, the portfolio risk is generalized into the so-called tail amplitude. The optimal portfolio is then obtained by using a simulated annealing heuristic to search for the minimum portfolio risk at a given level of portfolio return. Compared to the traditional MMV model, results show that this approach provides less risky optimal portfolios with better diversification.